Question

Analyze the conditional statement below and complete the instructions that follow. You will receive the trophy if you win the championship match. Identify the hypothesis and the conclusion of the conditional statement. hypothesis: you will receive the trophy; conclusion: you win the championship match hypothesis: you do not win the championship match; conclusion: you will not receive the trophy hypothesis: you win the championship match; conclusion: you will receive the trophy hypothesis: you will not receive the trophy; conclusion: you do not win the championship match

Answer 1

The correct hypothesis and conclusion for the given conditional statement is:

hypothesis: you win the championship match.

conclusion: you will receive the trophy.

Explanation:

We know that a conditional statement is represented by symbols p and q as:

If p then q. ( or p→q)

where p is the hypothesis statement and q is the conditional.

Here we are given conditional statement as:

" You will receive the trophy if you win the championship match "

The hypothesis is a statement such that when it happens than it leads to some result called as conclusion.

Hence, here the hypothesis is:

" If you win the championship match "

and the conclusion that happens after winning the match is:

" You will receive the trophy "

Answer 2

This is a problem of logic. So we need to identify what the conditional statement means. In logic, there are several operators, one of them is the conditional operator. As the name implies, the conditional operator creates a compound statement that sets up a condition for something to be true. If the condition is met, the statement is true.

Symbol: →

Parts of Conditional: Two simple statements joined by the conditional symbol. The first simple statement in a conditional is called the antecedent and the second simple statement is called the consequent.

So let's analyze each case:

Case 1. Analyze the conditional statement and complete the instructions that follow.

Statement: You will receive the trophy if you win the championship match.

We can rewrite this in a standard form of the conditional operator, that is:

A→B: If you win the championship match then you will receive the trophy

A: You win the championship match
B: You will receive the trophy

Hypothesis: You win the championship match
Conclusion: You will receive the trophy

Case 2.

According to the problem we have:

Hypothesis: You will receive the trophy.
Conclusion: You win the championship match

A: You will receive the trophy.
B: You win the championship match

We can rewrite this in an standard form of the conditional statement, that is:

A→B: If you will receive the trophy then you win the championship match

Case 3.

According to the problem we have:

Hypothesis: You do not win the championship match.
Conclusion: You will not receive the trophy

A: You do not win the championship match.
B: You will not receive the trophy

We can write this in a conditional statement:

A→B: If you do not win the championship match then you will not receive the trophy

Case 4.

According to the problem we have:

Hypothesis: You win the championship match
Conclusion: You will receive the trophy

We can rewrite this in a conditional statement:

A: You win the championship match
B: You will receive the trophy

We can write this in a conditional statement:

A→B: If you win the championship match then you will receive the trophy

Case 5.

According to the problem we have:

Hypothesis: You will not receive the trophy
Conclusion: you do not win the championship match

A: You will not receive the trophy
B: You do not win the championship match

We can write this in a conditional statement:

A→B: If you will not receive the trophy then you do not win the championship match.